Complete phase diagrams, that is, showing the solid, liquid, and vapor phases, are calculated for 29 binary mixtures of Lennard-Jones molecules characterized by different sets of interaction parameters using the Gibbs-Duhem integration technique. The impact of including the possibility of a solid phase on the global phase behavior of such mixtures is investigated by comparing the complete phase behavior calculated by simulation to the global phase diagram calculated from a fluid-phase-only equation of state. Complete phase diagrams from each region of the global phase diagram are presented and compared with the fluid-phase-only phase behavior for the same mixture. It is found that for mixtures in which the components have greatly dissimilar critical temperatures, the presence of the solid phase significantly alters the fluid-phase equilibria. In those cases, the phase behavior classification based on experimental observations should differ from that predicted by an equation-of-state approach. (C) 2004 American Institute of Chemical Engineers.